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Stochastic differential equation for wave diffusion in random media

By Gabriele Gradoni, Roberto Pastore, Davide Micheli, Franco Moglie, Valter Mariani Primiani and Mario Marchetti

Abstract

In this work, we present a statistical analysis of the wave motion through random media with perfect spatial disorder of inclusions. It is assumed that such a disorder can be tackled with the random potential function theory, whence the propagation of waves naturally turns to a diffusion process. The associated Itoô drift-diffusion process, and its Fokker-Planck equation are derived. It is found that the “ensemble” wave, i.e., the collective wave motion, fluctuates in space as a geometric Brownian motion. Finally, the effect of a double-well potential with random (vibrating) valleys is studied qualitatively by the Monte Carlo method. In practice, this situation occurs for high concentration and perfect dispersion of conductive/dielectric fillers, i.e., whose location and orientation are completely randomized

Publisher: IEEE / Institute of Electrical and Electronics Engineers Incorporated:445 Hoes Lane:Piscataway, NJ 08854:(800)701-4333, (732)981-0060, EMAIL: subscription-service@ieee.org, INTERNET: http://www.ieee.org, Fax: (732)981-9667
Year: 2013
DOI identifier: 10.1109/ICEAA.2013.6632429
OAI identifier: oai:iris.univpm.it:11566/127462
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